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In circuits containing capacitors and inductors, if capacitors and inductors are connected in parallel, it may occur within a small period of time: the voltage of the capacitor gradually increases while the current gradually decreases; At the same time, the current of the inductor gradually increases, while the voltage of the inductor gradually decreases. And in another very short period of time: the voltage of the capacitor gradually decreases, while the current gradually increases; At the same time, the current of the inductor gradually decreases, while the voltage of the inductor gradually increases. The increase of voltage can reach a positive maximum value, and the decrease of voltage can also reach a negative maximum value. Similarly, the direction of current will also change in the positive and negative directions during this process, which is called electrical oscillation in the circuit.
The phenomenon of circuit oscillation may gradually disappear or remain unchanged. When the oscillation persists, we call it equal amplitude oscillation, also known as resonance.
The time during which the voltage across a capacitor or inductor changes by one cycle is called the resonance period, and the reciprocal of the resonance period is called the resonance frequency. So the resonant frequency is defined in this way.
It is related to the parameters of capacitor C and inductor L, namely: f=1/(2 * π * √ LC), corresponding to angular frequency w=2 * π * f=1/√ LC. At this point, XL=Xc, the circuit is purely resistive, and the modulus of the circuit impedance is minimized. When the input voltage Ui is constant, the current in the circuit reaches its maximum value and is in phase with the input voltage Ui. In theory, at this point Ui=Ur=U0, UL=Uc=QUi, where Q is called the quality factor of the circuit.
Resonant frequency - related parameters
The time during which the voltage of a capacitor or inductor changes by one cycle is called the resonance period, and the reciprocal of the resonance period is called the resonance frequency. The so-called resonant frequency is defined in this way. It is related to the parameters of capacitor C and inductor L, namely: f=1/√ LC.
How to calculate the resonant frequency of a circuit?
Resonant circuits have a characteristic that capacitance is equal to inductance, and the circuit is resistive
So there is ω L=1/ω C
Because LC has known conditions, the resonant frequency point can be calculated
The quality factor Q=ω L/R. If the quality factor is 28, then the parallel resonant circuit reduces the current by 28 times; If it is a series resonant circuit, then the voltage has increased by 28 times.
So the voltage at the currentseries resonance point is the applied voltage multiplied by the quality factor
If the known conditions tell you that the applied voltage is the peak value, then multiply it directly; If the known conditions tell you that the applied voltage is the effective value, then you need to multiply the calculated voltage by 1.414 to obtain the peak value.
